mass fractions of sodium metavanadate

sodium metavanadate | elemental composition

Find the elemental composition for sodium metavanadate in terms of the atom and mass percents: atom percent = N_i/N_atoms × 100% mass percent = (N_im_i)/m × 100% Plan: • Write the chemical formula and gather atomic masses from the periodic table. • Determine values for N_i, m_i, N_atoms and m using these items. • Finally, compute the percents and check the results. Write the chemical formula: NaVO_3 Use the chemical formula, NaVO_3, to count the number of atoms, N_i, for each element and find the total number of atoms, N_atoms: | number of atoms Na (sodium) | 1 O (oxygen) | 3 V (vanadium) | 1 N_atoms = 1 + 3 + 1 = 5 Divide each N_i by N_atoms to calculate atom fractions. Then use the property that atom fractions must sum to one to check the work: | number of atoms | atom fraction Na (sodium) | 1 | 1/5 O (oxygen) | 3 | 3/5 V (vanadium) | 1 | 1/5 Check: 1/5 + 3/5 + 1/5 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Na (sodium) | 1 | 1/5 × 100% = 20.0% O (oxygen) | 3 | 3/5 × 100% = 60.0% V (vanadium) | 1 | 1/5 × 100% = 20.0% Look up the atomic mass, m_i, in unified atomic mass units, u, for each element in the periodic table: | number of atoms | atom percent | atomic mass/u Na (sodium) | 1 | 20.0% | 22.98976928 O (oxygen) | 3 | 60.0% | 15.999 V (vanadium) | 1 | 20.0% | 50.9415 Multiply N_i by m_i to compute the mass for each element. Then sum those values to compute the molecular mass, m: | number of atoms | atom percent | atomic mass/u | mass/u Na (sodium) | 1 | 20.0% | 22.98976928 | 1 × 22.98976928 = 22.98976928 O (oxygen) | 3 | 60.0% | 15.999 | 3 × 15.999 = 47.997 V (vanadium) | 1 | 20.0% | 50.9415 | 1 × 50.9415 = 50.9415 m = 22.98976928 u + 47.997 u + 50.9415 u = 121.92826928 u Divide the mass for each element by m to calculate mass fractions. Then use the property that mass fractions must sum to one to check the work: | number of atoms | atom percent | mass fraction Na (sodium) | 1 | 20.0% | 22.98976928/121.92826928 O (oxygen) | 3 | 60.0% | 47.997/121.92826928 V (vanadium) | 1 | 20.0% | 50.9415/121.92826928 Check: 22.98976928/121.92826928 + 47.997/121.92826928 + 50.9415/121.92826928 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Na (sodium) | 1 | 20.0% | 22.98976928/121.92826928 × 100% = 18.86% O (oxygen) | 3 | 60.0% | 47.997/121.92826928 × 100% = 39.36% V (vanadium) | 1 | 20.0% | 50.9415/121.92826928 × 100% = 41.78%

Mass fraction pie chart